Engine oil systems may use piston squirters, sometimes called cooling jets, to provide jets of oil to cool and/or lubricate pistons. Most of the known systems use fixed displacement oil pumps to deliver the oil from an oil pan through a gallery or galleries to the piston squirters. The flow rate of a fixed displacement oil pump depends upon the speed the pump is turned, thus requiring that the piston squirters, or gallery or galleries, be equipped with check valves to regulate oil flow at low engine speeds to maintain oil pressure, and that the gallery or galleries be equipped with a relief valve for dumping excess oil back into the oil pan at high engine speed. For instance, most high-output diesel engines require the use of piston cooling jets that squirt oil on the underside of the pistons and provide cooling. Because of the limited supply of oil at low engine speeds, such engines use a valve to stop the flow of oil when oil pressure is below a predetermined level. To date, no known system has been developed to eliminate such valves from the piston squirters while providing efficient oil supply.